Paper Citation Record · LEDGER

Robustly Learning Monotone Generalized Linear Models via Data Augmentation

As of 14 August 2026, this Paper Citation Record lists 37 of 37 outbound references and 0 inbound Pith citation observations for arXiv:2502.08611.

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pith.paper-citation-record.v1
2502.08611 v2

Coverage vector

measured 37 of 37 reference resolution

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Source: paper_references, paper_reference_links, observed 2026-08-08T04:39:52.118701Z

measured 37 of 37 standing notices

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Source: scholarly_work_events, retraction_status_cache, observed 2026-08-14T06:32:32.682623+00:00

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Reference resolution

37 of 37 outbound references displayed

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External citation measurements

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Outbound references

Observation 78651e0f-217c-4ba7-abf2-cd140941f2a4 · outbound

This paper cites an unresolved cited work.

Robustly Learning Monotone Generalized Linear Models via Data Augmentation Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-08T04:39:52.676965Z

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Observation c74728b3-ecbe-4932-9d0e-146a3877e445 · outbound

This paper cites (a) For anyt, s >0, TtTsg = Ttsg.

Robustly Learning Monotone Generalized Linear Models via Data Augmentation (a) For anyt, s >0, TtTsg = Ttsg

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T04:39:52.663035Z

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Observation 24e600aa-fd13-422f-9ec8-70c142580413 · outbound

This paper cites The Ornstein–Uhlenbeck semigroup induces an operatorL applying to functionsf ∈ L2(N ), defined below.

Robustly Learning Monotone Generalized Linear Models via Data Augmentation The Ornstein–Uhlenbeck semigroup induces an operatorL applying to functionsf ∈ L2(N ), defined below

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T04:39:52.649791Z

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Observation 422a55a8-56bf-4d64-9165-fdce8bd8999b · outbound

This paper cites an unresolved cited work.

Robustly Learning Monotone Generalized Linear Models via Data Augmentation Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-08T04:39:52.635610Z

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Observation 9d258136-6ba1-47d6-b3f9-cce633345afe · outbound

This paper cites We use Fact B.4 to prove the following Lemma B.5: Lemma B.5.

Robustly Learning Monotone Generalized Linear Models via Data Augmentation We use Fact B.4 to prove the following Lemma B.5: Lemma B.5

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T04:39:52.621189Z

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Observation f4440137-b352-4d55-a5b7-ac8804f0f4b7 · outbound

This paper cites an unresolved cited work.

Robustly Learning Monotone Generalized Linear Models via Data Augmentation Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-08T04:39:52.606196Z

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Observation 77bc4017-1435-4628-85db-06c7f0b978c6 · outbound

This paper cites an unresolved cited work.

Robustly Learning Monotone Generalized Linear Models via Data Augmentation Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-08T04:39:52.593413Z

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Observation 681f72c5-7133-493a-977d-d195c09ca855 · outbound

This paper cites Finally, the following facts about Gaussian distribution are useful to our paper: Fact B.7(Stein’s Lemma (Stein, 1981)).

Robustly Learning Monotone Generalized Linear Models via Data Augmentation Finally, the following facts about Gaussian distribution are useful to our paper: Fact B.7(Stein’s Lemma (Stein, 1981))

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T04:39:52.579409Z

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Observation 56aae35a-1cb8-4f5d-9422-8d70a904aae8 · outbound

This paper cites Therefore, we have that Pr z∼N (0,1) [|σ((1 + r)z) − Tδσ((1 + r)z)| ≥ϵ] ≤ Pr z∼N (0,1) [|σ(z) − Tδσ(z)| ≥ϵ] + 2r.

Robustly Learning Monotone Generalized Linear Models via Data Augmentation Therefore, we have that Pr z∼N (0,1) [|σ((1 + r)z) − Tδσ((1 + r)z)| ≥ϵ] ≤ Pr z∼N (0,1) [|σ(z) − Tδσ(z)| ≥ϵ] + 2r

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T04:39:52.565588Z

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Observation aeb02ce1-79b0-48da-901e-bfbca3a9885d · outbound

This paper cites an unresolved cited work.

Robustly Learning Monotone Generalized Linear Models via Data Augmentation Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-08T04:39:52.551188Z

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Observation ac798f20-f6c3-4698-9354-7e404417b581 · outbound

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Robustly Learning Monotone Generalized Linear Models via Data Augmentation Unresolved cited work

Reference 11

Resolution: unresolved; raw_fallback, observed 2026-08-08T04:39:52.537954Z

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Observation a43d3f32-8c90-4bd3-9865-b5486314edb2 · outbound

This paper cites an unresolved cited work.

Robustly Learning Monotone Generalized Linear Models via Data Augmentation Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-08T04:39:52.524656Z

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Observation 28de6cd1-b1f7-4e21-95ef-5fc4e024e0cd · outbound

This paper cites an unresolved cited work.

Robustly Learning Monotone Generalized Linear Models via Data Augmentation Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-08-08T04:39:52.510860Z

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Observation df2058a8-b811-483c-92f7-011fafaa252e · outbound

This paper cites Let ¯σ(z) = sign(σ(z)) min{|σ(z)|, p Bσ,4/ϵ}, which is an activation in the(B, L)-Regular class.

Robustly Learning Monotone Generalized Linear Models via Data Augmentation Let ¯σ(z) = sign(σ(z)) min{|σ(z)|, p Bσ,4/ϵ}, which is an activation in the(B, L)-Regular class

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T04:39:52.497953Z

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Observation f02c028e-6098-4d30-9103-879cb453a6ac · outbound

This paper cites Similarly, let ¯σ(z) = sign(σ(z)) min{|σ(z)|, eR(4r log(4) + log(R4/ϵ2))r} Denote for simplicityBσ := eR(4r log(4) + log(R4/ϵ2))r Then, ¯σ is a (Bσ, L)-Regular activation.

Robustly Learning Monotone Generalized Linear Models via Data Augmentation Similarly, let ¯σ(z) = sign(σ(z)) min{|σ(z)|, eR(4r log(4) + log(R4/ϵ2))r} Denote for simplicityBσ := eR(4r log(4) + log(R4/ϵ2))r Then, ¯σ is a (Bσ, L)-Regular activation

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T04:39:52.484439Z

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Observation 8193a9e0-1e60-403f-9994-576b1066bac3 · outbound

This paper cites Then, since|σ′| ≤b, we have∥σ′∥L2 ≤ b.

Robustly Learning Monotone Generalized Linear Models via Data Augmentation Then, since|σ′| ≤b, we have∥σ′∥L2 ≤ b

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T04:39:52.470762Z

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Observation e00e8a62-a08d-42be-960e-53166938bd8f · outbound

This paper cites augmented loss.

Robustly Learning Monotone Generalized Linear Models via Data Augmentation augmented loss

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T04:39:52.455006Z

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Observation b977bdef-6c1a-415c-b1cc-8f17c7714207 · outbound

This paper cites Plugging the above bounds for the casesk = 0, 1 back into Equation (14) completes the proof.

Robustly Learning Monotone Generalized Linear Models via Data Augmentation Plugging the above bounds for the casesk = 0, 1 back into Equation (14) completes the proof

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T04:39:52.441661Z

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Observation 58c01e05-d964-4293-a59f-2a0dc75f9e5d · outbound

This paper cites an unresolved cited work.

Robustly Learning Monotone Generalized Linear Models via Data Augmentation Unresolved cited work

Reference 19

Resolution: unresolved; raw_fallback, observed 2026-08-08T04:39:52.427134Z

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Observation d1a0bad5-5852-448e-84bf-11b07b58992a · outbound

This paper cites Assume that w(t+1) is still far away fromw∗ and θt+1 ≳ ζ(cos θt+1), meaning that we still need to further decrease the angle betweenw(t+1) and w∗.

Robustly Learning Monotone Generalized Linear Models via Data Augmentation Assume that w(t+1) is still far away fromw∗ and θt+1 ≳ ζ(cos θt+1), meaning that we still need to further decrease the angle betweenw(t+1) and w∗

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T04:39:52.414132Z

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Observation dacc47fe-88fc-44d6-8047-c606fa5c228a · outbound

This paper cites an unresolved cited work.

Robustly Learning Monotone Generalized Linear Models via Data Augmentation Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-08T04:39:52.399768Z

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Observation 71b8c381-3628-4fae-97f5-308eacc26ead · outbound

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Robustly Learning Monotone Generalized Linear Models via Data Augmentation Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-08T04:39:52.386371Z

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Observation be6b4319-df6d-42a3-802d-41a17ca3e730 · outbound

This paper cites The proof of Claim F.16 is deferred to Appendix F.2.3.

Robustly Learning Monotone Generalized Linear Models via Data Augmentation The proof of Claim F.16 is deferred to Appendix F.2.3

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T04:39:52.372250Z

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Observation e7a70ec1-c20d-40f3-9497-e9a3e74f9ffd · outbound

This paper cites an unresolved cited work.

Robustly Learning Monotone Generalized Linear Models via Data Augmentation Unresolved cited work

Reference 24

Resolution: unresolved; raw_fallback, observed 2026-08-08T04:39:52.357555Z

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Observation b4fa2b1c-f7df-4d76-9c86-ba4f2f4888b8 · outbound

This paper cites an unresolved cited work.

Robustly Learning Monotone Generalized Linear Models via Data Augmentation Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-08-08T04:39:52.343948Z

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Observation 0d587b77-fd81-45a8-9c03-6047caa8a39e · outbound

This paper cites 51 Proof of Claim F.16.Since ρ1, ρ <1, we only need to show thatρ2 1(1 − ρ4) ≥ 1 − ρ4.

Robustly Learning Monotone Generalized Linear Models via Data Augmentation 51 Proof of Claim F.16.Since ρ1, ρ <1, we only need to show thatρ2 1(1 − ρ4) ≥ 1 − ρ4

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T04:39:52.330490Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation e0fb5687-790f-4fe3-9c4b-7f5f1792aca2 · outbound

This paper cites Therefore, our goal is to prove that (ρ2 + C(1 − ρ2)/M2)(1 − ρ2)(1 + ρ2) ≥ (1 + ρ2 + C(1 − ρ2)/M2)(1 − ρ2)(1 − C/M 2).

Robustly Learning Monotone Generalized Linear Models via Data Augmentation Therefore, our goal is to prove that (ρ2 + C(1 − ρ2)/M2)(1 − ρ2)(1 + ρ2) ≥ (1 + ρ2 + C(1 − ρ2)/M2)(1 − ρ2)(1 − C/M 2)

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T04:39:52.315430Z

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Observation 2f055acf-17ca-4ffb-a604-013a191fd4c9 · outbound

This paper cites Proof of Claim F.17.For any fixedρ ∈ (0, 1), let us define h(M ) = (ρ2 + C(1 − ρ2)/M2)(1 − ρ4) 1 − (ρ2 + C(1 − ρ2)/M2)2.

Robustly Learning Monotone Generalized Linear Models via Data Augmentation Proof of Claim F.17.For any fixedρ ∈ (0, 1), let us define h(M ) = (ρ2 + C(1 − ρ2)/M2)(1 − ρ4) 1 − (ρ2 + C(1 − ρ2)/M2)2

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T04:39:52.299701Z

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Observation 0d492e5d-acdc-4e8b-a2df-5581c7d85616 · outbound

This paper cites Claim F.18.Let ρ2 ≥ 1 − C/M 2 and ρ2 1 = ρ2 + C(1 − ρ2)/M2.

Robustly Learning Monotone Generalized Linear Models via Data Augmentation Claim F.18.Let ρ2 ≥ 1 − C/M 2 and ρ2 1 = ρ2 + C(1 − ρ2)/M2

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T04:39:52.283946Z

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Observation 35e1fe2f-ecc4-42f6-a69e-5826e6f10d10 · outbound

This paper cites Inequality (i) is due to the facts that(t2 i + t2 j − 2ρ2 1titj) ≥ 0 for any ti, tj ∈ R and that 1/(1 − ρ4.

Robustly Learning Monotone Generalized Linear Models via Data Augmentation Inequality (i) is due to the facts that(t2 i + t2 j − 2ρ2 1titj) ≥ 0 for any ti, tj ∈ R and that 1/(1 − ρ4

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T04:39:52.269784Z

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Observation f1004f44-1a60-4590-bae6-548d17a5e176 · outbound

This paper cites an unresolved cited work.

Robustly Learning Monotone Generalized Linear Models via Data Augmentation Unresolved cited work

Reference 31

Resolution: unresolved; raw_fallback, observed 2026-08-08T04:39:52.254531Z

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Observation 27feba61-b4d9-4c06-a609-2eef43a85b02 · outbound

This paper cites This is without loss of generality, as follows from Claim C.7.

Robustly Learning Monotone Generalized Linear Models via Data Augmentation This is without loss of generality, as follows from Claim C.7

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T04:39:52.238679Z

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Observation 670444ef-c4e9-4adb-b5a8-9f0d4c9f841a · outbound

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Robustly Learning Monotone Generalized Linear Models via Data Augmentation Unresolved cited work

Reference 33

Resolution: unresolved; raw_fallback, observed 2026-08-08T04:39:52.221473Z

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Observation 6a7ad4e1-9414-431e-9e44-312ae7717b24 · outbound

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Robustly Learning Monotone Generalized Linear Models via Data Augmentation Unresolved cited work

Reference 34

Resolution: unresolved; raw_fallback, observed 2026-08-08T04:39:52.206312Z

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Observation c6f86aae-3faa-44f1-a825-d0f9bdcfce5a · outbound

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Robustly Learning Monotone Generalized Linear Models via Data Augmentation Unresolved cited work

Reference 35

Resolution: unresolved; raw_fallback, observed 2026-08-08T04:39:52.189644Z

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Observation 222d75b5-c480-4344-a154-cdc066f10c44 · outbound

This paper cites an unresolved cited work.

Robustly Learning Monotone Generalized Linear Models via Data Augmentation Unresolved cited work

Reference 36

Resolution: unresolved; raw_fallback, observed 2026-08-08T04:39:52.174191Z

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Observation 20048e4e-2f5b-4b64-9583-cb6121d81b3b · outbound

This paper cites In the rest of the proof, we will denote byM the smallest value in [0, ¯M ] such that Ez∼N [(σ(z) − σ(M ))21{z ≥ M }] ≥ C1ϵ.

Robustly Learning Monotone Generalized Linear Models via Data Augmentation In the rest of the proof, we will denote byM the smallest value in [0, ¯M ] such that Ez∼N [(σ(z) − σ(M ))21{z ≥ M }] ≥ C1ϵ

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T04:39:52.157685Z

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